Choose the correct option and justify your choice: 2tan30°/1-tan230° = ? (A) cos 60° (B) sin 60° (C) tan 60° (D) sin 30°

Answer: (C) tan 60°

Substitute the of tan 30° in the given equation

2 tan30°/1-tan230°

Trigonometry Values Table

Trigonometry values for angles 0°, 30°, 45°, 60°and 90°, with respect to sin, cos, tan, cot, sec, cosec functions, taking an example of the right-angle triangle.

Angle

00

300 450 600

900

Sin θ 0 1/2 1/√2 √3/2 1
Cos θ 1 √3/2 1/√2 1/2 0
Tan θ 0 1/√3 1 √3
Cot θ √3 1 1/√3 0
Sec θ 1 2/√3 √2 2
Cosec θ 2 √2 2/√3 1

The value of tan tan 30° = 1/√3

2tan30°/1-tan230° = 2(1/√3)/1-(1/√3)2

2tan30°/1-tan230° = (2/√3)/(1-1/3)

2tan30°/1-tan230°= (2/√3)/(2/3)

2tan30°/1-tan230° = √3

2tan30°/1-tan230° = tan 60°

The value of the given equation is equivalent to tan 60°

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